intertidal ﬁnger bars at el puntal, bay of santander, spain ... · the bar system is located in...

Earth Surf. Dynam., 2, 349–361, 2014www.earth-surf-dynam.net/2/349/2014/doi:10.5194/esurf-2-349-2014© Author(s) 2014. CC Attribution 3.0 License.

Intertidal finger bars at El Puntal, Bay of Santander,Spain: observation and forcing analysis

E. Pellón, R. Garnier, and R. Medina

Environmental Hydraulics Institute (IH Cantabria), Universidad de Cantabria, Santander, Spain

Correspondence to:E. Pellón ([email protected]) and R. Garnier ([email protected])

Received: 15 October 2013 – Published in Earth Surf. Dynam. Discuss.: 13 November 2013Revised: 2 May 2014 – Accepted: 11 May 2014 – Published: 26 June 2014

Abstract. A system of 15 small-scale finger bars has been observed, by using video imagery, between 23 June2008 and 2 June 2010. The bar system is located in the intertidal zone of the swell-protected beaches of El PuntalSpit, in the Bay of Santander (northern coast of Spain). The bars appear on a planar beach (slope= 0.015) withfine, uniform sand (D50 = 0.27 mm) and extend 600 m alongshore. The cross-shore span of the bars is determinedby the tidal horizontal excursion (between 70 and 130 m). They have an oblique orientation with respect tothe low-tide shoreline; specifically, they are down-current-oriented with respect to the dominant sand transportcomputed (mean angle of 26◦ from the shore normal). Their mean wavelength is 26 m and their amplitude variesbetween 10 and 20 cm. The full system slowly migrates to the east (sand transport direction) with a mean speedof 0.06 m day−1, a maximum speed in winter (up to 0.15 m day−1) and a minimum speed in summer. An episodeof merging has been identified as bars with larger wavelength seem to migrate more slowly than shorter bars.The wind blows predominantly from the west, generating waves that transport sediment across the bars duringhigh-tide periods. This is the main candidate to explain the eastward migration of the system. In particular, thewind can generate waves of up to 20 cm (root-mean-squared wave height) over a fetch that can reach 4.5 km athigh tide. The astronomical tide seems to be important in the bar dynamics, as the tidal level changes the fetchand also determines the time of exposure of the bars to the surf-zone waves and currents. Furthermore, the riverdischarge could act as input of suspended sediment in the bar system and play a role in the bar dynamics.

1 Introduction

Transverse bars are morphological features attached to theshore that appear with a noticeable rhythmicity along thecoast of sandy beaches. They have been identified in manytypes of environments and have been observed with a widerange of characteristics; therefore a classification of the ex-isting bar systems is necessary. This is not straightforwardsince these features can be classified using many criteria suchas their geometry (length scale, orientation with respect tothe shoreline), their dynamics (formation time, migration) ortheir hydro-morphological environment. Alternatively, clas-sification can be made based on the physical processes gov-erning their formation and their dynamics, although these aresometimes not well understood.

The most documented and observed transverse bar type isprobably the “TBR” (“transverse bar and rip”) described byWright and Short (1984), which imposes a cuspate shape onthe shoreline, sometimes called mega-cusps (Thornton et al.,2007). They sometimes appear with an oblique orientationwith respect to the shoreline (Lafon et al., 2002; Castelleet al., 2007). The TBR are typically linked to outer morpho-logical patterns; specifically, they form due to the onshoremigration of a crescentic bar (Ranasinghe et al., 2004; Gar-nier et al., 2008). They are generally found on intermediatewave-dominated beaches of open coasts and they have wave-lengths (distance between two bars) of 100–500 m, and areassociated with the presence of rip currents flowing offshorebetween two bars. Remarkably, the study of Goodfellow andStephenson (2005) shows that these systems can also appear,at smaller scales, in lower-energy environments (40 km li-mited fetch).

Published by Copernicus Publications on behalf of the European Geosciences Union.

350 E. Pellón et al.: Intertidal finger bars at El Puntal, Bay of Santander, Spain

Table 1. Transverse bar types and main characteristics.

Type Beach Mean Bar Cross-shore Bar Migration Reference oftype wave wave span orientation rateb observed

height length (m)a (m day−1) bars(m)a (m)a

TBR Intermediate > 0.5 100–500 < 150 Normal, 5c Wright and Short (1984)(transverse wave-dominated oblique Lafon et al. (2002)bars and beaches Ranasinghe et al. (2004)rips) Goodfellow and Stephenson (2005)d

Castelle et al. (2007)Thornton et al. (2007)

Large- Low-energy < 0.5 ∼ 100 ∼ 1000 Normal 1 Niederoda and Tanner (1970)scale beaches, wide or Gelfenbaum and Brooks (2003)finger (∼ 1 km) slightly Levoy et al. (2013)bars with gentle oblique

slope (0.002)

Finger Intermediate > 0.5 50–100 < 100 Oblique 40 Konicki and Holman (2000)bars of wave-dominated up-current- Ribas and Kroon (2007)intermediate beaches oriented Ribas et al. (2014)beaches

Small- Very fetch- < 0.1 < 50 < 100 Oblique Lack Falqués (1989)scale limited down-current- of Bruner and Smosna (1989)low-energy (< 10 km) oriented data Nordstrom and Jackson (2012)finger Present studybars

a Typical observed values.b The values given for the migration rates are the maximum alongshore velocities detected.c Some studies have detected much larger (∼ 50 m day−1) alongshore migration rates of crescentic bars (van Enckevort et al., 2004) and mega-cusps (Galal and Takewaka, 2008), butthese systems are not clearly coupled with TBR.d These authors identify smaller scale TBR in a low-energy environment.

Here we will focus on “(transverse) finger bars”, whichdiffer from the TBR because they do not emerge from off-shore bathymetric features but are assumed to form “alone”.Moreover, they are not necessarily associated with rip cur-rents. Regarding their geometry, the main difference with theTBR is that the finger bars are long-crested, i.e. their cross-shore extent is generally larger than their wavelength. Weidentify three types of finger bars (Table1).

1. The first type of finger bar was identified by Niedorodaand Tanner (1970). We will refer to them as “large-scale finger bars” because of their large cross-shore span(∼ 1 km). Their wavelength is∼ 100 m and they ap-pear in low-energy environments (mean wave height< 0.5 m) on very wide (∼ 1 km) beaches with a gen-tle slope (0.002). They are oriented almost perpendic-ular to the shore or with a slight obliquity, in bothmicro- and macro-tidal environments (Gelfenbaum andBrooks, 2003; Levoy et al., 2013).

2. Although finger bars are often associated with very lowwave energy (Wijnberg and Kroon, 2002), a second typeof finger bar can be observed in intermediate morpho-logical beach states (Konicki and Holman, 2000; Ribas

and Kroon, 2007; Ribas et al., 2014). They coexist, ata smaller wavelength (typically 50–100 m), with otherrhythmic morphologies present in the surf zone, such aswith TBR and with crescentic bars. One of the partic-ularities of these “finger bars of intermediate beaches”is that they have an oblique up-current orientation withrespect to the mean alongshore current (Ribas et al.,2007).

3. Finally, a third type of finger bar, the “small-scale low-energy finger bars”, appears for very low wave energy infetch-limited environments (fetch< 10 km) with wave-lengths of∼ 10 m and a cross-shore span (10–100 m)that depends on the horizontal tidal excursion (Brunerand Smosna, 1989; Garnier et al., 2012). These bars arenot strictly normal to the shore (Falqués, 1989; Nord-strom and Jackson, 2012) but seem to be down-current-oriented with respect to the dominant sand transport(Bruner and Smosna, 1989), which is opposite to thefinger bars of intermediate beaches.

The processes of generation and evolution of finger barsare probably different depending on their type, and, in partic-ular, their orientation. It is thought that finger bars generally

Earth Surf. Dynam., 2, 349–361, 2014 www.earth-surf-dynam.net/2/349/2014/

E. Pellón et al.: Intertidal finger bars at El Puntal, Bay of Santander, Spain 351

migrate in the direction of sediment transport, but trans-port direction is not always identified, possibly due to thelack of field data. The theoretical modelling studies of Ribaset al. (2003) and Garnier et al. (2006) have shown differ-ent mechanisms to explain the dynamics of up- and down-current-oriented bars by considering forcing due to waves.Ribas et al. (2012) successfully applied their model to fin-ger bars of an intermediate beach, based on continuous ob-servations obtained from video imagery. However, the dy-namics of finger bars appearing in low-energy environmentsis poorly understood, especially concerning the small-scalelow-energy finger bars because (1) the forcing is difficultto determine, with forces due to wind, waves and tidal cur-rents all similar in magnitude in very limited fetch envi-ronments, and (2) there has been no continuous, long-termsurvey of such systems. Some observation studies on large-scale finger bars have measured mean migration rates of lessthan 2 m month−1 (Gelfenbaum and Brooks, 2003; Levoyet al., 2013) and maximum speeds of 1 m day−1 (Levoy et al.,2013). For the case of small-scale low-energy finger bars,only the preliminary study of Garnier et al. (2012) has giveninformation on the dynamics of such systems, but the migra-tion rates detected are overestimated due to strong noise inthe data.

The objective of this contribution is to gain insight into thedynamics of small-scale low-energy transverse bars by per-forming a continuous survey of finger bars detected in theBay of Santander, Spain, and by analysing the possible forc-ing mechanisms. These finger bars are located in the inter-tidal zone, and the survey is performed by using video im-ages at low tide. Section 2 presents the field site and the dataset obtained by video imagery. Section 3 describes the char-acteristics and the dynamics of the bar system. Section 4 re-ports the forcing analysis based essentially on wind data. Theconclusions are listed in Sect. 5.

2 Field site and video imagery

2.1 Study site

El Puntal Spit is part of the natural closure of the Bay of San-tander (Fig.1). This bay is one of the largest estuaries on thenorthern coast of Spain (Cantabrian Sea). The closure of thebay is composed of two natural formations, the MagdalenaPeninsula to the north-west, and El Puntal Spit to the north-east. This spit is a sand accumulation which extends fromeast to west over approximately 2.5 km. Historically, morethan 50 % of the surface of this bay has been filled in, reduc-ing the tidal prism and changing the morphological equilib-rium of El Puntal (Losada et al., 1991), which tends to extendwestward. However, for navigation purposes (Medina et al.,2007), the entrance channel is periodically dredged, and thusthe west end of El Puntal is maintained artificially.

There are numerous studies on El Puntal analysing themorphodynamics of the northern face and the west end

Figure 1. (a) Location of Santander,(b) map of the bay,(c) El Pun-tal at high tide, and(d) El Puntal at low tide. Images from GoogleEarth; Landsat;© 2009 GeoBasis-DE/BKG;© 2013 Google; USDept of State Geographer; Data SIO, NOAA, U.S. Navy, NGA,GEBCO;© 2013 DigitalGlobe.

(Losada et al., 1992; Kroon et al., 2007; Requejo et al., 2008;Medellín et al., 2008, 2009; Gutiérrez et al., 2011), but thelower-energy southern face remains unstudied. The incom-ing swell from the Cantabrian Sea only reaches the northernface of the spit (Medellín et al., 2008). The southern pro-tected beaches of El Puntal are part of the bay and are locatedin a low-energy mesotidal environment. The maximum rangeof the semidiurnal tide is 5 m. Recent hydrodynamic studies(Bidegain et al., 2013) have reported an ebb-oriented meanannual flow of up to 0.1 m s−1 in the channel to the south ofEl Puntal. This flow is mainly driven by the (ebb-dominated)tidal current and by the flow from the Miera River, which en-ters the bay at the east end of the El Puntal Spit. In the shal-lower areas the mean flow is much weaker and wind effectscan become predominant (Bidegain et al., 2013), especiallyif we take into account the waves that can be generated overa fetch of up to 4.5 km from the south-west direction. Thefetch is highly variable over a tidal cycle due to the numerous

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intertidal shoals in the bay (Fig.1b), which can reduce themaximum fetch to 200 m at low tide.

The finger bar system is located in the intertidal zone ofthe beach on the southern side of the spit. Aerial images showa system of 15 well-developed finger bars that is fully sub-merged at high tide (Fig.1c) and fully emerged at low tide(Figs.1d and2a). At mid-tide the coastline exhibits a cuspateshape (Fig.2) and processes of wave refraction and wavebreaking are observed (Fig.2c).

The alongshore extent of the bar system is less than 600 mand the mean bar wavelength is about 25 m. The cross-shoreextent of the bars is controlled by the horizontal tidal excur-sion and is larger in the middle of the domain (130 m) than onthe lateral sides (70 m). The bars are almost parallel and havean oblique orientation with respect to the low-tide coastline.The bar angle with respect to the low-tide shore normal isabout 25◦ toward the southeast (where 0◦ would correspondto shore normal, transverse bars). However, the western endof the system is more irregular, with slight changes in barorientation and bifurcations (Fig.1d).

The intertidal beach where the bars appear is planarwith a constant slope of approximately 0.015. The offshoreboundary of the bars is delimited by a steep slope that ends inthe subtidal channel. Sediment sampling has shown the samegrain size on bars and troughs withD50 = 0.27 mm.

2.2 Video imagery and bar detection

In the last few decades, video monitoring systems have beenincreasingly used to study the shoreline around the world(Holman et al., 1993). To obtain geometric data of the barsystem, the images of the Horus video imagery system wereused (Medina et al., 2007). This system is composed offour cameras located on the roof of Hotel Real, 91 m a.s.l.and 1.5 km from the study area (Fig.3a). The Horus sta-tion was established in 2008 and takes images every 10 min.In the present study only camera 2 was used (Fig.3b). Thepixel resolution on the study area is variable on the along-shore direction, with values from 4.5 to 6.6 m pixel−1. In thecross-shore direction the resolution is around 0.5 m pixel−1.One daily image of the bar system has been selected at lowtide between 23 June 2008 and 2 June 2010, which is thelongest period found without long interruptions in the imagedatabase. All the interruptions were of less than 6 consecu-tive days and were due to technical problems (27 days) andpoor meteorological conditions (fog 18 days, strong wind3 days and bad sharpness 85 days). The geometry of the barswas extracted on 577 days, which is 81 % of the time.

Each bar has been digitised manually by selecting threepoints along the trough at the upper, middle and lowest end ofeach bar (Fig.4). Three points were found to describe the po-sition and orientation sufficiently. These digitised data wererectified using seven geographic control points (GCP), estab-lished for the Horus system, thus giving geographic coordi-nates of each digitised bar.

Figure 2. Photos at(a, b) low tide and with(c, d) rising tide. Pic-tures taken from the east end of the study area(a, c), and from thewest end(b, d). Capture date: 25 February 2012.

Figure 3. Horus video system.(a) Cameras on the roof of HotelReal.(b) Image taken by camera 2.

The data processed by Garnier et al. (2012) have been re-analysed in order to correct an apparent periodic movementdue to sun shadows in the bars. The amplitude of this periodicmovement is of the order of the pixel resolution, and it hasbeen found that its period is related to the capture times. Thisapparent movement seems to be a systematic error linked tothe different sun positions at low tide during the fortnightlycycle of neap-spring tides, which causes different shadowsdue to the bars and different light reflections in the wet areas.This light shadowing/reflection also occurs for fixed struc-tures present in the surrounding areas. This allowed us topartially correct this spurious movement.

For further analysis, a local, approximately shore-parallelcoordinate system has been defined with the alongshore,y axis at 113◦ from north (Fig.4). Within the new coordinatesystem, the mean shoreline position now is approximatelyparallel to they axis during most of the tidal cycle. To bet-ter understand the behaviour of the finger bars, the digitisedbars are then subsampled atx1 = 45,x2 = 65,x3 = 85, andx4 = 105 m over the length of the alongshore domain (y1–y4 axes; see Fig.4). These positions have been chosen togive complete cross-shore coverage of the bars, and each oneis representative of one level of the beach profile (Fig.5c).



Figure 4. Coordinate system and bar digitisation. Thex andy axesstand for the cross-shore and the alongshore direction respectively.The colour points represent the digitised data (each bar is repre-sented by three points); blue, red and green are the lowest, the mid-dle and the upper points of the bars respectively. The bar positions(P1–P4) are defined along they1–y4 axes, atx1 = 45, x2 = 65,x3 = 85, andx4 = 105 m respectively (see positions of bar 6, inwhite). Image from Google Earth,© 2013 DigitalGlobe.

2.3 3-D geometry

The Horus system captures one image of the study area every10 min. This means that the path of the shoreline can be ob-served along the tidal cycle with high frequency. To extractinformation about the 3-D geometry of the finger bar system,a reconstruction of the intertidal bathymetry of the study areahas been performed by mapping the shoreline from every im-age. This must be done on a day with perfect conditions, asthe meteorological conditions and image sharpness need tobe excellent. Furthermore, the tide should have the highestrange possible, allowing the extraction of a large intertidalregion, and this must occur during daylight hours.

On good days, the shoreline is digitised and rectified oneach image. To obtain the bathymetry we assume that the sealevel measured at the tide gauge of Santander (less than 2 kmaway) is the same as the level of the shoreline in the studyarea. The tide level (with respect to the local Santander Har-bour datum,Z) at the time of each image is associated withthe rectified shoreline from that image, obtaining an intertidalbathymetry.

2.4 Piecewise regression of the bar movement

The method proposed here to find the time-dependent migra-tion rates is based on piecewise regressions. This allows usto focus on the medium-term movements rather than on thedaily fluctuations. The time series of the bar position for eachbar at each cross-shore position has been decomposed intosegments of variable length. The segment length has been setin order to minimise the error between the piecewise segmentand the measured positions. After this decomposition, eachbar is represented by several segments of different lengths

(the segmentk has a length ofTk). For each segment, wecan therefore obtain the approximate bar migration rateVk,which is the migration rate of this bar during the time intervalTk.

Considering that, at a timet , N segments are obtained(whereN is the number of bars of the system at this timet , multiplied by 4, which is the number of cross-shore posi-tions studied), the time-dependent migration rate of the barsystemVm (which is the average of the speeds, at this timet ,of all the bars on all the cross-shore positions) is computedas

Vm(t) =

N(t)∑i=1

V̂i(t)

N(t), whereV̂i(t) =

{Vk, if t ∈ Tk

0, otherwise.(1)

3 Bar characteristics and dynamics

3.1 Bathymetry reconstruction

A bathymetry reconstruction has been done on 12 days withexcellent meteorological conditions. Figure5a shows thebathymetry obtained for 24 June 2008, the day with thebest image quality. Cross-shore profiles of this bathymetry(Fig. 5c) show that the bars only appear on the region of theintertidal beach profile which has constant slope of 0.015.The extraction of alongshore profiles from these bathyme-tries allows us to measure the amplitude of the bars, whichoscillates between 10 and 20 cm. These profiles also show theasymmetry of the bars (Fig.5b) with steeper slopes on the leesides (relative to the migration direction), in agreement withprevious studies (Gelfenbaum and Brooks, 2003).

3.2 Bar dynamics

During the 2-year study period the position and geometryof 15 bars were digitised daily. Figure6 shows the posi-tion of the bar system along they3 axis once the digitiseddata have been corrected, rectified and transformed to the de-scribed coordinate system (Fig.4). Taking into account thatthe pixel resolution on the study area is of about 5 m pixel−1

in the alongshore direction, the small oscillations visible inFig. 6 are not deeply analysed, as they could be either phys-ical or measurement errors. The bar system is persistent intime, appearing in all the observed images with similar geo-metric characteristics, but the entire system slowly migratesto the east. As a result of the eastward migration a new barbecomes visible at the western end of the study area (bar 1,Fig. 6). Although aerial images and the migration of the sys-tem suggest that the bars are formed at the west of the studyarea, the formation area is not included in the present resultsas it is hidden by the dune (Fig.5a). At the eastern end of thearea, the last bar decays and slowly disappears. In addition,during the study period, only one episode of merging of twobars into one has been detected, on 28 March 2009 (bars 5–6,Fig. 6).



Figure 5. (a) Bathymetry reconstruction with videoed shoreline po-sitions during rising tide (24 June 2008). The north–west area with-out data is the shadowed area by the dune, from the point of view ofthe camera.(b) Alongshore profile of the bed level.(c) Cross-shoreprofiles of the bed level and cross-shore positions of they1–y4 axes.Image from Google Earth,© 2013 DigitalGlobe.

3.2.1 Time-averaged characteristics

The digitised and rectified data allow the daily measurementof the bar wavelength. The bar wavelength is computed as thedifference between the positions (on theyi axis) of two con-secutive troughs. For each bar, the wavelength has been aver-aged over the complete study period (Fig.7). The wavelengthis approximately constant for each bar during the study pe-riod (standard deviation,σ , around 4 m for all bars), butvaries between bars, with a minimum of 15 m and a maxi-mum of 36 m. The mean wavelength of the whole bar systemis 25.8 m.

Similarly, the variability of the mean bar angle is low, withσ around 5◦ for each bar. The mean angle of the system,measured from thex axis, is 26.4◦, with a maximum angleof 34◦ at the western end, decreasing to a minimum of 17◦ atthe eastern end (Fig.7). The bars are not straight in plan view,so their angle has also been studied by splitting the bars intotwo parts, the upper (onshore) half and the lower (offshore)half. The upper part of all the bars has a lower angle with theshore normal (mean of the whole system of 23◦), while thelower part has higher angles (mean of 31◦).

The time series of bar position is almost continuous andallows us to compute the time-averaged migration rate of thesystem, which is obtained by linear regression. The mean

Figure 6. Evolution of the bar system. Time series of the bar po-sition along they3 axis. The thin, discontinuous lines represent themeasured position. The thick segments represent the piecewise re-gression of the measured position. The number to the left of eachline indicates the bar number.

Figure 7. Time-averaged wavelength, angle and migration rate ofeach bar. The bar angles are measured from the shore normal to theeast. Positive values of the bar speeds represent movements of thebars to the east.

speed of each bar (for the whole study period) is shown inFig. 7. All the bars of the system slowly migrate to the east,with a mean speed of 6 cm day−1 (approximately one wave-length per year). The maximum migration rate is obtainedfor the bar with the shortest wavelength (8 cm day−1, bar 5)that merges with the next bar, which is longer and slower(bar 6). In general, the longer the wavelength, the slower themigration rate. This is in agreement with previous studies ontransverse bars (Garnier et al., 2006).

There are noticeable differences in the dynamics and inthe characteristics of the first five bars (western bars) com-pared with the eastern bars. The western bars (close to theformation zone) are more irregular in shape, with a largermean angle (5◦ larger), a smaller wavelength (20 m mean)and a corresponding higher migration rate. The eastern barsare well defined and remarkably parallel. Their cross-shorespan decreases as they approach the decaying zone.



3.2.2 Time-dependent migration rates

Each bar signal has been decomposed into 10 segments bymeans of the piecewise regression described in Sect. 2.4(Fig. 6). It was found that 10 is the best number to repre-sent the medium-term movement of the bar and to filter thedaily fluctuations. As we are analysing 2 years of data, themean segment length is 70 days.

The migration rate of the bar systemVm, computed with(Eq. 1), is not constant in time with maximum migration ratesin winter (Fig.8). The maximum speeds, about 0.15 m day−1,are reached during the first winter studied (2009), while dur-ing the second winter (2010) the maximum speeds are lowerthan 0.1 m day−1. During summer the system migration isslower, with negative speeds for summer 2008, and migrationrates lower than 0.01 m day−1 for summer 2009. The nega-tive speeds (i.e. migration to the west) found in summer 2008can be due to limitations in the computation ofVm. Specif-ically, the accuracy of the piecewise regression is expectedto be lower at the beginning and end of the time series, dueto the lack of previous/subsequent data. The negative migra-tion rate is obtained for the first segment of the bars only;therefore this result may not be realistic.

4 Forcing analysis

4.1 Forcing candidates

The migration to the east of the bar system indicates a domi-nant forcing coming from the west. The wind data have beenextracted from the SeaWind (Menéndez et al., 2011) reanal-ysis database. Figure9a shows the wind rose, and the timeseries of the wind speed is displayed in Fig.9c. The pre-dominant wind is from the west, reaching values of up to25 m s−1. The wind from the east is also frequent but lessenergetic, with speeds lower than 15 m s−1. The mean windspeed is 5 m s−1.

Other studies on transverse bars (Ribas et al., 2003) sug-gest that waves are the main forcing that controls their dy-namics. The study area is protected from the incoming swell(Medellín et al., 2008) and the waves that can act on the barsystem are generated locally. According to estuarine studiesthese wind waves can have a significant effect in the sedimenttransport (Green et al., 1997). Here, wind waves are gener-ated over a maximum fetch of 4.5 km (from the south-westof the study area). Toward the south and south-east the fetchis reduced by the proximity of land.

During the survey period, the tidal range oscillates be-tween 1 and 5 m (Fig.9d). Maximum values of the tidal cur-rent in the channel (offshore of the bar system) occur duringspring tides, with values of up to 0.25 m s−1. In the chan-nel the mean (residual) flow is ebb-oriented, but the resid-ual tidal current is small in the intertidal areas. Computationsperformed (not shown) with an H2D model (Bárcena et al.,2012) show that the maximum residual current (obtained dur-

Figure 8. Vm (thick black line), time-dependent migration rate ofthe entire bar system (average of all coloured lines).Vk (colourlines), individual bar migration rate (the colours correspond toFig. 6). (a) Vk for bars 3–8.(b) Vk for bars 9–14.

Figure 9. (a) Wind rose. (b) Wave rose.(c–f) Time series ofthe (c) wind speedW , and the daily averaged(d) tidal range,(e) river flow rate and(f) root-mean-squared wave height of thewind wavesHrms.



ing spring tides) is lower than 0.01 m s−1 in the study area.Although the residual current is small, the tide can have aneffect on the bar dynamics because tidal currents can causesediment stirring (which is stronger during mid tides) andbecause of the changes in water level. Firstly, the fetch isstrongly dependent on the water level (Green et al., 1997)according to the emersion and submersion of the numerousintertidal shoals during the tidal cycle, and this is taken intoaccount in the wave computations (see Sect. 4.2.1). Secondly,the changes in tidal level affect the time of bar submersion(that is larger during neap tides) and the volume of sand thatcan be transported (larger if high tide coincides with strongwinds/waves). This will be taken into account in the sedimenttransport computations by including the tidal correction fac-tor (see further explanations in Sect. 4.3.2).

Hydrodynamic studies of the Santander Bay have high-lighted the effect of the water discharge produced by theMiera River (to the east of the study area) in the annual meancurrent magnitude in the bay (Bidegain et al., 2013). Time se-ries of the daily averaged river flow rate are shown in Fig.9e.Bidegain et al. (2013) have shown that, although the effectof the river is strong in the channel (ebb-oriented flow), thecurrent produced close to the bar system is weak. However,the river discharge can play a role in the bar dynamics as it islinked to a strong sediment supply, which can act as an inputof suspended sediment to the bar system.

4.2 Wind acting on water surface

4.2.1 Wave computation

The wind waves over the system have been simulated fromthe wind speed and direction by using the SWAN model(Booij et al., 1999). In the computations, changes in tidallevel affecting the fetch have been included. The time seriesof the wind waves has been obtained with an interpolationtechnique based on radial basis functions (RBF), a schemewhich is convenient for scattered and multivariate data (Ca-mus et al., 2011). Results of the root-mean-squared (rms)wave heightHrms of the waves approaching the bar systemare displayed in Fig.9b (wave rose) and in Fig.9f (timeseries of the daily averagedHrms). The waves arrive fromthe west-south-west and south-west 65 % of the time, with ameanHrmsof 5 cm and a period of 1.5 s. During the westwardwindstorms the waves can extend to 20 cm from the west-south-west, with a period of 3 s. The other 35 % of the timethe waves come from the east-south-east, withHrms lowerthan 7 cm and periods below 1.7 s. The meanHrms from thissector is less than 2 cm with a period of 1.2 s.

4.2.2 Wind stress vs wind-wave stress forcing

The previous studies on transverse bars, where the waves ap-pear to be the main forcing, usually focus on wave parame-ters to relate the dynamics of the bars with the incident waveforcing, for example the alongshore component of the wave

energy flux (e.g. Castelle et al., 2007; Price and Ruessink,2011) or the wave radiation stress (e.g. Ribas and Kroon,2007).

Here, the effect of the local wind is also analysed by com-puting the alongshore component of the wind shear stressacting on the water surface (Figs.10a and11a), defined as(Dean and Dalrymple, 1991)

Ty = −ρCfW2cosθw, (2)

whereρ is the water density (ρ = 1025 kg m−3); Cf is thefriction coefficient, equal to 1.2×10−6; W is the wind speed;andθw is the incoming wind angle (from the shore normal).

In order to compare the relative effect of the wind stressand of the wave radiation stress, we define the alongshorewave stress,Sy = Sxy/Xb (Figs. 10b and11b). Sxy is thealongshore component of the wave radiation stress (Longuet-Higgins and Stewart, 1964) andXb is the surf-zone width. ByconsideringXb = Hrms/(β γb), we obtain

Sy =ρg

16

Hrms

βγbsinθ cosθ, (3)

whereg is the gravitational acceleration (g = 9.81 m s−2),γb is the breaking coefficient for irregular waves (γb = 0.42,Thornton and Guza, 1983),β is the beach slope (β = 0.015)andθ is the offshore wave angle (from the shore normal).Sy

is an approximation of the term∂Sxy/∂y in the alongshoremomentum balance equation, a term that is equivalent toTy

in the same equation.Figure11a and b show the seasonal variability ofSy andTy

respectively. The comparison of both figures shows that bothforcings are of the same order of magnitude and can there-fore play a role in the bar dynamics, althoughSy is twiceas large asTy . Only the wind stress seasonal analysis showsmore highly energetic conditions in winter 2009 than in win-ter 2010, in accordance with the results of the migration rate.However, the wind stress shows more highly energetic con-ditions in autumn than in winter, while the migration rateshows lower values in autumn 2009 than in winter 2009.The wave stress seasonal analysis shows lower differencesbetween autumns and winters, with larger values still beingin the autumn.

4.3 Sediment transport

The relationship between the bar migration and the along-shore component of the sediment transport is also investi-gated. We use a formulation based on the Soulsby and VanRijn formula (Soulsby, 1997). This formulation has beenused in modelling studies to explain the formation of differ-ent kinds of transverse bars (Ribas et al., 2012; Garnier et al.,2006).



Figure 10. Time series of the daily averaged(a) alongshore windstress (Ty , black) and(b) alongshore wave stress (Sy , black). Thegrey lines represent the behaviour of the bar migration rateVm thathas been rescaled with the above variables.

4.3.1 Soulsby and Van Rijn formula

Here, we assume that the general formulation of the along-shore component of the sediment transport is given by

q = α (Vwave+ Vwind) , (4)

whereα is the sediment stirring function,Vwave is the along-shore component of the wave- and depth-averaged currentdriven by the wind waves, andVwind is the alongshore com-ponent of the depth-averaged current driven by the localwind.

The alongshore current generated by the wind waves is ap-proximated from the formula presented by Komar and Inman(1970):

Vwave= 1.17(gHrms)0.5sinθbcosθb, (5)

whereθb is the wave angle at breaking. By using Snell’s lawand the dispersion relationship, Eq. (5) has been evaluated atthe breaking depth, defined asHrms/γb (γb = 0.42) fromthe incident wave angle computed with the SWAN model(Sect. 4.1).

The alongshore current generated by the wind is computedby assuming the alongshore momentum balance between thewind stress and the bottom friction in the case of a quadraticfriction law:

Vwind = ±

∣∣∣∣ Ty

ρcd

∣∣∣∣0.5

, (6)

wherecd is the hydrodynamic drag coefficient set ascd =

0.005.The stirring function in Eq. (4) is approximated with the

Soulsby and Van Rijn formula (Soulsby, 1997) as

α =

{AS

(Ueq− Ucrit

)2.4 if Ueq > Ucrit

0 otherwise,(7)

whereAS is a coefficient that represents the suspended loadand the bed load transport andUcrit is the critical velocity

Figure 11. Seasonal variability of(a) alongshore wind stress (Ty )and(b) alongshore wave stress (Sy ). The black lines represent thebehaviour of the bar migration rateVm that has been rescaled withthe above variables. The bottom axes indicate the seasons, fromsummer 2008 to spring 2010.

above which the sediment can be transported.AS andUcritdepend essentially on the sediment characteristics and onthe water depth (for more details see Soulsby, 1997; Garnieret al., 2006). The equivalent stirring velocity is defined as

Ueq =

(U2

wind + V 2wave+

0.018

CdU2

b

)0.5

, (8)

whereUb is the wave orbital velocity amplitude at the bottom(computed at wave breaking),Cd is the morphodynamic dragcoefficient computed with the formula of Soulsby (1997) andUwind is the modulus of the current generated by the wind:

Uwind =

(Cf

cdW2

)0.5

. (9)

4.3.2 Tidal correction factor

Although the tidal level variations have been included tocompute the incoming wave time series, the sediment trans-port formula defined in Sect. 4.3.1 does not take into accountthat the bars can be emerged, and are therefore inactive, dur-ing part of a tidal cycle. If strong winds and high waves (de-spite the limited fetch) coincide with the time of emersion,they will have no effect and the effective sediment transportshould be zero. Furthermore, the time of submersion dependson the tidal range. During neap tides the bar system is af-fected by the marine dynamics almost 100 % of the time be-cause the full emersion of the bars occurs only when the tideis at its lowest level (during a short time period). However,during spring tides, the active time period is reduced because



the tide falls lower and the bars stay emerged for a longertime.

These effects have been quantified by means of a tidal cor-rection factor (αt), ranging from 0 to 1, which evaluates howexposed the bars are due to the stirring resulting from the hy-drodynamics. The corrected transport formula is then com-puted as

q t= αt q; (10)

αt varies every hour, depending on the surf-zone width (Xb)and on the tidal level (ηt). It is computed by using the follow-ing formula (see Fig.12):

αt =

0 if Z3 < ηt

Z3 − ηt

Z3 − Z2αt,max if Z2 < ηt < Z3

αt,max if Z1 < ηt < Z2

ηt − Z0

Z1 − Z0αt,max if Z0 < ηt < Z1

0 if ηt < Z0,

(11)

whereαt,max quantifies the ratio between the surf-zone width(corresponding to theHrms) and the cross-shore span of thebars, representing the percentage of the bars that could bewithin the active surf zone,

αt,max =Xb

L=

Hrms

βγbL, (12)

where L is the mean cross-shore span of the bars (L =

100 m) andXb is the width of the active surf zone (Fig.12).Z0, Z1, Z2 andZ3 are defined as (see Fig.12)

Z0 = 2.5 m = level of the bar lower end

Z1(t) = Z0 + h∗(t) = 2.5+ γ −1b Hrms(t)

Z2 = 3.7 m = level of the bar upper end

Z3(t) = Z2 + h∗(t) = 3.7+ γ −1b Hrms(t).

(13)

Z0 andZ2 (levels of the bar lower end and upper end) areconstant and determined from the 3-D-geometry (Fig.5).Z1 andZ3 depend on the active depthh∗ defined as (h∗

=

Hrms/γb).To better understand these formulas, let us consider a day

with constant wave height. The tidal correction factor is ma-ximum (αt = αt,max) when the maximum depth at the bars islarger than the active depth (ηt ≥ Z1) and when the sea leveldoes not exceed the upper end of the bars (ηt ≤ Z2). Thismeans that the complete surf-zone width is located over thebars. Furthermore, the sediment transport over the bars van-ishes if the sea level does not reach the lower end of the bars(ηt ≤ Z0, i.e. too shallow) and if the minimum water depthat the bars is larger than the active depth (ηt ≥ Z3, i.e. toodeep).

Figure 12. Parameters for the calculation of the tidal correctionfactor (αt), which depends on the tidal level (ηt); the mean cross-shore span of the bars (L); the active depth (h∗); the surf-zone width(Xb); and the level of the bar lower end (Z0), the bar upper end (Z2)and the levelsZ1 andZ3, which vary with the wave height (Hrms).

Figure 13. Time series of: the tidal correction factorαt (red dots);and the tidal range (greyscale, vertical bars).

From our observations, the tidal factor never reaches 1(Fig. 13). αt = 1 could occur for strong stormy conditionsif the surf-zone width is as large as the bar width L (Hrms >

0.5), and if it coincides with high tide (ηt = Z2). Figure13shows thatαt reaches its maximum values during neap tides,as was expected, generally as the tidal level is close toZ2 alarger part of the day. During spring tides, the time duringwhich the tidal level is betweenZ3 andZ0 is highly reduced.Consequently, the tidal factor is generally minimum.

4.3.3 Results

In order to analyse the correlation betweenq and the bar mi-gration rateVm, the time-dependent sediment transport ratemust be computed. First, we integrate the sediment trans-port over the time intervalsTk, for each segment that char-acterises the bar movement (as explained in Sect. 3.2.2), andthen we apply an equation equivalent to Eq. (1) for that sed-iment transport data. The obtained time series of the time-dependent sediment transport is shown in Fig.14.

Figure 14a, which displays the sediment transport with-out the tidal correction, shows that the sediment transport isweaker in spring 2009 than in spring 2010, corresponding toa smaller migration rate. However, the seasonal average ofq

shows similar values for autumn–winter 2009 and autumn–winter 2010, while the migration rate results show lowervalues during 2010. The correlation coefficient obtained isr = 0.75.

The addition of the tidal factor improves the results(Fig. 14b) increasing the correlation coefficient tor = 0.8.All correlations obtained are highly significant (p < 0.001).



Figure 14. Sediment transport evaluation. Analysis of(a) along-shore component of sediment transportq (without tidal correction),and(b) qt (with tidal correction). The grey areas show the season-ally averaged transport and the red lines show the time-dependentsediment transport time series (obtained by averaging over theTk

intervals). The black lines represent the behaviour of the bar migra-tion rateVm that has been rescaled with the above variables. Thecorrelation coefficient of both lines is shown in the bottom rightcorner. The bottom axes indicate the seasons, from summer 2008 tospring 2010.

The seasonal analysis shows higher values of sediment trans-port during autumn–winter 2009 than autumn–winter 2010,corresponding with higher time-dependent migration ratesduring autumn–winter 2009. Again, the sediment transportcomputed in spring 2009 is lower than in spring 2010, cor-responding well with the smaller migration rates measuredin spring 2009. The time-dependent sediment transport timeseries ofq t (Fig. 14b) follows the main shape of the mea-sured time-dependent migration rate. The bigger differencesare found at the beginning and end of the study period, wherethe time-dependent migration rates are less reliable, as ex-plained in Sect. 3.2.2. In particular, none of the formulasused managed to predict the negative (westward) migrationreported during summer 2008, but, as previously mentioned,these negative migration rates may be not realistic.

Figure9e shows the flow rate of Miera River. This flowrate is greater during winter 2009 than winter 2010, so thefaster migration rate of the bars during this period couldbe influenced by the river discharge, possibly because it isa source of sediment. However, tests performed by includingadditional sediment stirring due to the river flow do not showimprovement in the results.

5 Conclusions

A small-scale finger bar system has been identified on the in-tertidal zone of the swell-protected beach of El Puntal Spitin the Bay of Santander (northern coast of Spain). The beachis characterised by a constant slope of 0.015 and by uniformsand withD50 = 0.27 mm. This system appears on the flat in-tertidal region, which extends over 600 m on the alongshoredirection and between 70 and 130 m on the cross-shore di-rection (the cross-shore span is determined by the tidal hori-zontal excursion).

A system of 15 bars was observed by using the Horusvideo imaging system during 2 years (between 23 June 2008and 2 June 2010). The bar system has been digitised fromdaily images at low tide. The data set is almost continuous,with good quality data 81 % of the time and a maximum con-tinuous period of time without data of no more than 6 days.

The geometric characteristics of the system are almostconstant in time. The mean wavelength of the bar system is26 m and the bar amplitude is between 10 and 20 cm. More-over, the bars have an oblique orientation with respect to thelow-tide shoreline, with a mean angle of 26◦ to the east fromthe shore normal. We noticed differences in the geometryalong the domain: the western bars (first half) are more ir-regular and have smaller wavelength than the eastern bars(second half).

The full system slowly migrates to the east (against the ebbflow) with a mean speed of 6 cm day−1 that varies betweenbars. In general, larger wavelength bars migrate more slowly,in agreement with previous studies (Garnier et al., 2006).An episode of merging of two bars was observed on 28March 2009: the bar with the smallest wavelength is fasterand merges with the next bar. Bars form on the western endof the system, migrate east and then decay at the eastern end.

A detailed analysis of the bar motion, from a piecewiseregression of the bar positions, has shown that bars migratemore quickly in winter than in summer, with maximum mi-gration rates obtained in winter 2009 (0.15 m day−1). Somenegative speeds (migration to the west) have been computed(during summer 2008), but this result could be an effect ofthe limitations of the piecewise regression at the beginningand end of the time series.

The primary forcing mechanism that is acting on the bardynamics is the wind over the water surface. Offshore ofthe bar system, the mean (annual) flow is ebb-oriented (tothe west), because of the Miera River discharge and the as-tronomical tide. However, in the intertidal zone their effectson the mean flow vanish. There, wind shear stress and windwaves generated over a fetch of up to 4.5 km at high tideseem to determine the direction of the alongshore transport.

Although the residual tidal current is weak, the tide seemsto be important in the bar dynamics as the tidal range changesthe mean (daily) fetch as well as the time of exposure of thebars to the marine dynamics. Furthermore, the river discharge



could act as input of suspended sediment in the bar systemand play a role in the bar dynamics.

The correlation between the bar migration and the along-shore component of the sediment transport has been anal-ysed by using the Soulsby and Van Rijn formulation. The in-clusion of a tidal correction factor, simulating that the activetime depends on the tidal level and the wave height, improvesthe results.

Finally, the bar system is persistent and neither formationnor destruction events of the entire system have been ob-served. Further studies are necessary to understand the for-mation processes and the full dynamics of these small-scalefinger bars. In situ measurements of the hydrodynamics andsediment concentrations, as well as numerical morpholog-ical modelling, are essential in order to deepen our under-standing. The bar system here has an oblique down-currentorientation with respect to the migration direction and hassimilar characteristics and dynamics to the system describedby previous theoretical (modelling) studies that consider theforcing due to waves only (e.g. Garnier et al., 2006). How-ever, in our estuarine environment, the dynamics are morecomplex as the actions of different forcings are of the sameorder of magnitude.

Acknowledgements. The authors thank Puertos del Estado(Spanish Government) for providing tide-gauge data. The workof R. Garnier is supported by the Spanish Government throughthe “Juan de la Cierva” programme. This research is part of theANIMO (BIA2012-36822) project, which is funded by the SpanishGovernment. The authors thank the editor, G. Coco, and thereferees, F. Ribas and E. Gallagher, for their useful comments.

Edited by: G. Coco

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